JACOBI_EIGENVALUE Eigenvalues and Eigenvectors of a Symmetric Matrix

JACOBI_EIGENVALUE is a C++ library which computes the eigenvalues and eigenvectors of a real symmetric matrix.

Given a real symmetric NxN matrix A, JACOBI_EIGENVALUE carries out an iterative procedure known as Jacobi's iteration, to determine a N-vector D of real, positive eigenvalues, and an NxN matrix V whose columns are the corresponding eigenvectors, so that, for each column J of the eigenmatrix:

```        A * Vj = Dj * Vj
```

Languages:

JACOBI_EIGENVALUE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

TEST_EIGEN, a C++ library which implements test matrices for eigenvalue analysis.

TEST_MAT, a C++ library which defines test matrices, some of which have known determinants, eigenvalues and eigenvectors, inverses and so on.

Reference:

1. Gene Golub, Charles VanLoan,
Matrix Computations, Third Edition,
Johns Hopkins, 1996,
ISBN: 0-8018-4513-X,
LC: QA188.G65.

List of Routines:

• JACOBI_EIGENVALUE carries out the Jacobi eigenvalue iteration.
• R8MAT_DIAG_GET_VECTOR gets the value of the diagonal of an R8MAT.
• R8MAT_IDENTITY stores the identity matrix in an R8MAT.
• R8MAT_IS_EIGEN_RIGHT determines the error in a (right) eigensystem.
• R8MAT_NORM_FRO returns the Frobenius norm of an M by N R8MAT.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8VEC_PRINT prints an R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.

Last revised on 15 July 2013.